Abstract
This paper discusses the method of Liu Hui (3rd century) for evaluating the ratio of the circumference of a circle to its diameter, now known as π A translation of Liu’s method is given in the Appendix. Also examined are the values for or given by Zu Chongzhi (429–500) and unsurpassed for π a millenium. Although the method used by Zu is not extant, it is almost certain that he applied Liu’s method. With the help of an electronic computer, a table of computations adhering to Liu’s method is given to show the derivation of Zu’s results. The paper concludes with a survey of circle measurements in China. © 1986 Academic Press, Inc.
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References
Ang Tian Se. 1977. Chinese computation with the counting-rods. Papers on Chinese Studies, University of Malaya 1, 97–109.
Bai Shangshu [ap]. 1982. Cong Wang Mang Jiang qi dao Liu Xin yuan lu [er] [From Wang Mang’s measuring vessel to Liu Xin’s ratio of circumference to diameter]. Beijing daxue xuebao, No. 2, 75–79.
Bai Shangshu 1983. Jiu zhang suanshu zhushi [es] [Annotations on Nine chapters of the mathematical art]. Beijing: Kexue chubanshe.
Beckmann, P. 1970. A history of ir (pi). All page references are to the second edition, Boulder, Colo.: Golem, 1971.
Gupta, R. C. 1975. Some ancient values of pi and their use in India. Mathematics Education 9, 1–5. He Shaogeng [bb]. 1983. Method for determining segment areas and evaluation of a. In Ancient
China’s technology and science. Compiled by the Institute of the History of Natural Sciences
Chinese Academy of Sciences. Beijing: Foreign Language Press.
Heath, T. L. (ed.). 1897. The works of Archimedes. All page references are to the reissued edition, New York: Dover, 1953.
Heath, T. L. 1921. A history of Greek mathematics. 2 vols. London/New York: Oxford Univ. Press (Clarendon).
Lam Lay-Yong. 1969. The geometrical basis of the ancient Chinese square-root method. /.sis 61, 92101.
Lam Lay-Yong and Shen Kangsheng. 1985. The Chinese concept of Cavalieri’s principle and its applications. Historia Mathematica 12, 219–228.
Li Di [bg]. 1962. Da kexuejia Zu Chongzhi [et] [The great scientist Zu Chongzhi]. Shanghai: Renm in chubanshe.
Li Di [bg]. 1982. Jiu zhang suanshu zhengming wentide gai shu [eu] [A summary of the various views
on the Jiu zhang suanshu]. In Jiu zhang suanshu yu Liu Hui [cw] [The Jin zhang suanshu and Liu Hui], Wu Wenjun [cv], ed., pp. 28–50. Beijing: Shifan daxue chubanshe.
Mikami, Y. 1913. The development of mathematics in China and Japan. All page references are to the second edition, New York: Chelsea, 1974.
Needham, J. 1959. Science and civilisation in China. Vol. 3. Cambridge: Cambridge Univ. Press.
Neugebauer, O. 1952. The exact sciences in antiquity. All page references are to the second edition, Providence, R.I.: Brown Univ. Press, 1957.
Qian Baocong [al]. 1923. Zhongguo suan shu zhong zhi zhoulu yanjiu [ex] IA study of ar in Chinese mathematical texts]. In Qian Baocong kexueshi lunwen xuanji [cy] [Selected essays of Qian Baocong on the history of Chinese science], pp. 50–74. All page references are to the 1983 book edition, Beijing: Kexue chubanshe 1983.
Qian Baocong (ed.). 1963. Suanjing shi shu [cz] [Ten mathematical manuals]. Shanghai: Zhonghua shuju.
Qudan Xida [da]. 729. Kaiyuan zhan jing [aq] [Kaiyuan treatise on astrology].
Ruan Yuan [db]. 1799. Chou ren zhuan [dc] [Biographies of mathematicians and scientists]. In Guoxue jiben congshu. Taipei: Shangwu yinshuguan, 1968.
Song shu [ar]. [Standard history of the Liu Song dynasty]. 1973 edition. Beijing: Zhonghua shuju. Sui shu [y] [Standard history of the Sui dynasty]. 1973 edition. Beijing: Zhonghua shuju.
Sun Zhifu [an]. 1955. Zhongguo gudai shuxue jia guanyu yuanzhoulu yanjiu de chengjiu [dd] [Achievements in the research of it by ancient Chinese mathematicians]. Shuxue Tongbao, No. 5, 5–12.
Wagner, D. 1978. Doubts concerning the attribution of Liu Hui’s commentary on the Chiu-chang suan-shu. Acta Orientalia 39, 199–212.
Wang, L., and Needham, J. 1955. Homer’s method in Chinese mathematics: Its origins in the root-extraction procedures of the Han dynasty. T’oung Pao 43, 345–401.
Xu Chunfang [ao]. 1957. Zhong suan jiade jihexue yanjiu [de] [Research on geometry by Chinese mathematicians]. Hong Kong.
Yan Dunjie [as]. I936a. Sui shu lull zhi Zu Chongzhi yuan lu ji shi shi [df] [An analysis of records for it by Zu Chongzhi as found in the harmonics and calendar chapters of Sui shu]. Xue yi zazhi [dg] (Shanghai) 15, No. 10 27–57.
Yan Dunjie 1936b. Zhongguo suanxuejia Zu Chongzhi ji qi yuanzhou lu zhi yanjiu [dh] [Chinese mathematician Zu Chongzhi and his work on ir]. Xue yi zazhi [dg] (Shanghai) 15, No. 5, 37–50.
Youschkevitch, A. P., and Rosenfeld, B. A. 1973. Al-Kashi (or Al-Kashani), Ghiyath al-din Jamshid Mas’ud. In Dictionary of scientific biography, Vol. 7, pp. 255–262. New York: Scribner’s.
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Lay-Yong, L., Tian-Se, A. (2000). Circle Measurements in Ancient China. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3240-5_5
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DOI: https://doi.org/10.1007/978-1-4757-3240-5_5
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